A reply to the discussion “Accelerated growth of calcium silicate hydrates: Experiments and simulations” by S. Bishnoi and K. Scrivener

Abstract

We sincerely thank Dr. Bishnoi and Prof. Scrivener for their com-ments [1] on Nicoleau's paper[2]. This discussion contributessigni cantly in clarifying the current debate about alternatives tomodel the cement hydration kinetics. In spite of our initial intereston the accelerating part of the hydration[2], the main point discussedby Bishnoi and Scrivener concerns the limitation of growth kinetics ofC-S-H during the alite hydration, leading to the post-peak decelera-tion in isothermal calorimetry. Our reply will therefore also focus onthis part of the hydration process, where different models are todayin opposition. Doing so, we answer the ve different points claimedby Bishnoi et al. in[1].1. On factors limiting the growthThe cornerstone condition for a proper description of the alite hy-dration kinetics is to take into account (1) the nucleation and growthof C-S-H and (2) the dissolution of alite[3]. The hydration kineticscannot be described only by a nucleation and growth process as inBishnoi's model[4] and in other models based on“Avrami-like” equa-tions discussed later in this reply. Besides in the original Garrault andNonat's model[5], the dissolution was also not considered since onlythe accelerating part of the hydration was addressed in this paper. Inthis part, the limitation by the dissolution is negligible. An extensionof this model including also the dissolution rate and the grain sizedistribution was recently proposed[6].In order to generate a limitation of the hydration rate, modelsbased on Avrami-like equations introduce some impingements tothe C-S-H growth. In particular, the Bishnoi's model asserts that thedeceleration of the growth originates with“impingements with C-S-H originating from different particles will affect nucleation and growthkinetics” as it has been rst proposed in[4] and also questionably as-sumed in[1]. This con guration is schematically depicted by the case1inFig. 1. This hindrance undergone by the C-S-H growth is termedas an inter-layers impingement. On the contrary, in the Garrault andNonat's model[5], there is also a hindrance but due to the collisionof growing clusters located on same grains. This can be termed asan intra-layer impingement (case 2 inFig. 1). Nevertheless, thehindrance is not suf cient to account for the complete deceleration;it is actually considered that the main contribution to this decelera-tion is the decrease of the dissolution rate due to the coverage ofthe alite surface by C-S-H[2,3,5]. The limitation of the dissolution isdescribed in Nicoleau's paper through a diffusion barrier resultingfrom the coverage of alite grains by C-S-H and parameterized by apermeability coef cient.The free space between cement grains is strongly affected by thegrain size distribution, as the water to alite ratio also does. Thegrain size distribution has therefore a considerable effect in case 1(Bishnoi's model) since the C-S-H growth and its limitation isdescribed by the lling of the free space around the cement grainsas it has been proposed in[4] and mentioned in [1]. As far as earlyhydration times are considered, the particle size distribution is notimportant in case 2 since the growth is described by clusters growingonto a single grain. The rst point debated by Bishnoi et al. is there-fore strictly dependent to their model. The question is now toconsider which model is more relevant for a proper description ofalite hydration. We recall in the following section several experimen-tal facts in favor of case 2.2. Effect of the water to cement ratioMore than 20 years ago, it was experimentally demonstrated rstby Damidot [7 9] in stirred and diluted suspensions and con rmedlater [10] by others that the water to cement (or the water to alite/C